We have our own Invasion Day (Waitangi) on February 6.
However we also have Matariki a new Public Holiday for Māori (Although everyone gets it) celebrated every year in late June or early July in Aotearoa to celebrate the first rising of the Pleiades star cluster. The dates vary from year to year, this year, Matariki will be celebrated on July 14.
I personally think we should drop the King's Birthday Holiday afterall they don't even get a Public holiday for it in the UK.